Why is there an expectation sign in the Bellman equation?
There needs to be an $E_{\pi}$ over the infinite discounted return term because of two reasons-


The policy could be stochastic in nature. That is, for any given state $s_t$ at time $t$, the policy $\pi(s_t)$ does not provide a deterministic action $a$, but rather, it provides us with a distribution over the possible next states, that is the action at time $t$, $a_t$ is distributed as-
$$a_t \sim \pi(s_t)$$
Even if the policy $\pi$ being followed by an agent is deterministic, there still needs to be an expectation over the behavior of the underlying stochastic MDP environment. That is, any action $a_t$, in general, only provides us with a distribution over the possible next states of the agent. That is, 
$$P(s_{t + 1} = s') = P_{\pi}(s' | s_t) = \sum_{a \in A} T(s,a,s') \times P_{\pi}(a_t = a)$$ 
Here $T(s, a, s')$ is the transition function for the MDP and the above equation captures the stochasticity arising from both 1 and 2.


As you see the expectation does not have to do with averaging over a collection of trajectories. However, that idea is often used in Monte-Carlo estimation of value functions. 

EDIT:
As pointed out in the comments, it is not correct to say that the expectation is not over a collection of trajectories.